Deriving gravitational potential energy (by bringing mass from infinity to r)

AI Thread Summary
The discussion centers on the derivation of gravitational potential energy (GPE) when bringing a mass from infinity to a distance r from a gravitational source. The user encounters confusion as their integration of force over distance yields a positive GPE, contradicting the expected negative value. Clarification is sought regarding the correct interpretation of force direction and the signs in the calculations. It is emphasized that the work done in moving the mass should reflect a negative potential energy, aligning with the principle that gravitational potential energy is defined as negative when considering the work done against gravitational attraction. The conversation highlights the importance of understanding force direction and the implications for energy calculations in gravitational systems.
Miraj Kayastha
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I understand the derivation of gravitational potential energy when an object is moved away from Earth but when I try to derive the formula for gpe by considering a test mass moving from infinity to r then I end up with a positive gravitational potential energy. Because integrating F.dr from infinity to r is equal to (magnitude of F) times (dr) times (cos 0) and I get a positive gravitational potential energy?

Can somebody show me the derivation of gpe considering a mass brought from infinity to r with detailed explanation (especially the signs)?
 
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Integrating F*dr from infinity to r gives you the work done. In the infinity the energy of system was 0. The work done gives you the change in kinetic energy. Since you got positive result, Ep + Ek = 0, therefor potential energy must be negative.
So everything is OK
 
I did not get my answer from that. I need the derivation
 
Miraj Kayastha said:
Because integrating F.dr from infinity to r is equal to (magnitude of F) times (dr) times (cos 0) and I get a positive gravitational potential energy?
What are you taking as your force F? What direction does it have?
 

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